An 4n-point Interpolation Formula for Certain Polynomials

TL;DR

This paper introduces a new 4n-point interpolation formula for specific polynomials, utilizing divided difference operators, and connects it to Jackson's summation formula through a determinantal interpretation.

Contribution

It presents a novel 4n-point interpolation formula applicable to certain polynomials, including Jackson's _8 o_7 summation, with a determinantal perspective based on Krattenthaler's identity.

Findings

Established a 4n-point interpolation formula for specific polynomials

Connected Jackson's _8 o_7 summation to a determinantal interpretation

Demonstrated the formula's applicability to Jackson's summation

Abstract

By using some techniques of the divided difference operators, we establish an 4n-point interpolation formula. Certain polynomials, such as Jackson's _8\phi_7 terminating summation formula, are special cases of this formula. Based on Krattenthaler's identity, we also give Jackson's formula a determinantal interpretation.